The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is
If the area of a square increases four times, then its side is not doubled.
If the area of a square increases four times, then its side is doubled
If the area of a square does not increases four times, then its side is not doubled
If the side of a square is not doubled, then its area does not increase four times
$( S 1)( p \Rightarrow q ) \vee( p \wedge(\sim q ))$ is a tautology $( S 2)((\sim p ) \Rightarrow(\sim q )) \wedge((\sim p ) \vee q )$ is a Contradiction. Then
Which of the following is a contradiction
The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :
Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$
Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.
The statement $A \rightarrow( B \rightarrow A )$ is equivalent to